本研究在建立一套雙足機器人的行走方法，以簡單的欠致動系統:賽格威（Segway）的零點動態為出發點，利用其特性設計機器人行走策略。在本論文一開始，進一步延伸到三連桿的機器人模型上，且在腳底額外多加了腳掌，即腳掌與地面的夾角形成一欠致動角度，來讓此模型的行走更接近一般人類的行走姿態。接著將一個完整的行走週期，細分成5個階段，包含抬腳、腳跟著地、腳尖離地的類人動態，在各階段有各自的控制目標及控制策略，利用到了ZMP的回授和軌跡規劃的方式，來完成雙足機器人一個週期的行走。最後透過模擬軟體來驗證此行走策略，初步已完成一欠致動雙足機器人的行走方法。

In this paper, the purpose is to establish a walking method for biped robot. By the zero dynamics with the simple underactuated system (Segway), we utilize the feature to design the walking strategy for biped robot. In the begin of this paper, we use the model of three-link robot, and add the sole in both feet, so there is an underactuated angle between the sole and the ground. By this way, we can make the biped robot walking more similar to nature human walking. After that, the full walking cycle was subdivided into five stages, including the humanoid motion like lift knee、heel landing、toes off the ground. At various stages has their own control objectives and control strategies, we utilize the ZMP (Zero Moment Point) feedback and trajectory planning to complete a walking cycle for biped robot. Finally, we use the simulation software to verify this walking strategy, and have preliminary completed a walking method for an underactuated biped robot.

[1]K. Hirai, M. Hirose, Y. Haikawa, T. Takenaka, "The development of Honda humanoid robot," Robotics and Automation, 1998. Proceedings. 1998 IEEE International Conference on , vol.2, no., pp.1321,1326 vol.2, 16-20 May 1998

[2]M. Vukobratović. Biped locomotion: dynamics, stability, control, and application. Berlin: Springer-Verlag, 1990. Print.

[3]K. Nagasaka, H. Inoue, M. Inaba, "Dynamic walking pattern generation for a humanoid robot based on optimal gradient method," Systems, Man, and Cybernetics, 1999. IEEE SMC '99 Conference Proceedings. 1999 IEEE International Conference on , vol.6, no., pp.908,913 vol.6, 1999

[4]J. Yamaguchi, S. Inoue, D. Nishino, A. Takanishi, "Development of a bipedal humanoid robot having antagonistic driven joints and three DOF trunk," Intelligent Robots and Systems, 1998. Proceedings., 1998 IEEE/RSJ International Conference on , vol.1, no., pp.96,101 vol.1, 13-17 Oct 1998

[5]S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Yokoi, H. Hirukawa, "A realtime pattern generator for biped walking," Robotics and Automation, 2002. Proceedings. ICRA '02. IEEE International Conference on , vol.1, no., pp.31,37 vol.1, 2002
[6]S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Harada, K. Yokoi, H. Hirukawa, "Biped walking pattern generation by using preview control of zero-moment point," Robotics and Automation, 2003. Proceedings. ICRA '03. IEEE International Conference on , vol.2, no., pp.1620,1626 vol.2, 14-19 Sept. 2003

[7]J. H. Kim, "Walking pattern generation of a biped walking robot using convolution sum," Humanoid Robots, 2007 7th IEEE-RAS International Conference on , vol., no., pp.539,544, Nov. 29 2007-Dec. 1 2007

[8]Y. Choi, D. Kim, Y. Oh, B. J. You, "Posture/Walking Control for Humanoid Robot Based on Kinematic Resolution of CoM Jacobian With Embedded Motion," Robotics, IEEE Transactions on , vol.23, no.6, pp.1285,1293, Dec. 2007

[9]T. Sugihara, Y. Nakamura, H. Inoue, "Real-time humanoid motion generation through ZMP manipulation based on inverted pendulum control," Robotics and Automation, 2002. Proceedings. ICRA '02. IEEE International Conference on , vol.2, no., pp.1404,1409 vol.2, 2002

[10]T. McGeer, “Passive dynamic walking,” International Journal of Robotics Research, vol. 9, no. 2, pp. 62–82, 1990.

[11]T. McGeer, "Passive walking with knees," Robotics and Automation, 1990. Proceedings., 1990 IEEE International Conference on , vol., no., pp.1640,1645 vol.3, 13-18 May 1990
[12]T. McGeer, “Passive Dynamic Biped Catalogue,” In Proceedings of the 2nd International Symposium of Experimental Robotics, pp.465-490, New York: Springer-Verlag , 1991.

[13]S. Collins, M. Wisse and A. Ruina, “A Three-Dimensional Passive-Dynamic Walking Robot with Two Legs and Knees,” The International Journal of Robotics Research, Vol. 20, No. 7, pp. 607-615, 2001.

[14]S. Collins, A. Ruina, R. Tedrake, M. Wisse, “Efficient Bipedal Robots Based On Passive-dynamic Walkers,” Science, Vol. 307, No. 5712, pp. 1082-1085, 2005.

[15]J. W. Grizzle, G. Abba, F. Plestan, "Asymptotically stable walking for biped robots: analysis via systems with impulse effects," Automatic Control, IEEE Transactions on , vol.46, no.1, pp.51,64, Jan 2001

[16]E. R. Westervelt, G. Buche, J. W. Grizzle, “Experimental Validation Of A Framework For The Design Of Controllers That Induce Stable Walking In Planar Bipeds,” The International Journal of Robotics Research, vol. 23, No. 6, pp. 559-582, 2004.

[17]C. Chevallereau, D. Djoudi, J. W. Grizzle, "Stable Bipedal Walking With Foot Rotation Through Direct Regulation of the Zero Moment Point," Robotics, IEEE Transactions on , vol.24, no.2, pp.390,401, April 2008
[18]C. Chevallereau, J. W. Grizzle, C.-L. Shih, "Asymptotically Stable Walking of a Five-Link Underactuated 3-D Bipedal Robot," Robotics, IEEE Transactions on, vol.25, no.1, pp.37,50, Feb. 2009

[19]T. Y. Wu, T. J. Yeh, "Optimal design and implementation of an energy-efficient, semi-active biped," Robotics and Automation,2008 .ICRA 2008. IEEE International Conference on, vol., no., pp.1252,1257, 19-23 May 2008

[20]T. Y. Wu, T. J. Yeh, "An experimental iterative learning strategy for a biped performing semi-active walking," Autonomous Robots and Agents,2009. ICARA 2009. 4th International Conference on, vol., no., pp.420,425, 10-12 Feb. 2009

[21]K. Nishiwaki, S. Kagami, Y. Kuniyoshi, M. Inaba, H. Inoue, "Toe joints that enhance bipedal and fullbody motion of humanoid robots," Robotics and Automation, 2002. Proceedings. ICRA '02. IEEE International Conference on, vol.3, no., pp.3105,3110, 2002

[22]R. Sellaouti, O. Stasse, S. Kajita, K. Yokoi, A. Kheddar, "Faster and Smoother Walking of Humanoid HRP-2 with Passive Toe Joints," Intelligent Robots and Systems, 2006 IEEE/RSJ International Conference on , vol., no., pp.4909,4914, 9-15 Oct. 2006

[23]Y. Ogura, K. Shimomura, H. Kondo, A. Morishima, T. Okubo, S. Momoki, H. Lim, A. Takanishi, "Human-like walking with knee stretched, heel-contact and toe-off motion by a humanoid robot," Intelligent Robots and Systems, 2006 IEEE/RSJ International Conference on , vol., no., pp.3976,3981, 9-15 Oct. 2006

[24] http://orthoteers.com/images/uploaded/images7/gait4.jpg

[25] http://world.honda.com/ASIMO/technology/

[26] http://www.aldebaran-robotics.com/en

[27]詹凱鈞，「欠致動雙足機器人動態行走之控制與實作」，國立清華大學動力機械工程學系碩士論文，2011

[28] http://www.segway.com

[29]葉展宏，「欠致動雙足機器人之動態行走」，國立清華大學動力機械工程學系碩士論文，2012

[30]E. R. Westervelt, J. W. Grizzle, C. Chevallereau, J. Choi and B. Morris, Feedback Control of Dynamic Bipedal Robot Locomotion(Control and Automation). Boca Raton: CRC Press, June 2007.